# [gmx-users] Deviations in free energies with slow growth (single and 3-step process)

David Mobley dmobley at gmail.com
Thu Feb 7 17:15:56 CET 2008

```Maik,

> I simulated a switching process (slow growth TI) over 10ns of ethane to
> methanol with hardcore slow-growth in water (365 TIP4P waters,PME) and
> in vacuum. The thermodynamic cycle of this calculation yields a DeltaG,
> which is in perfect agreement with the experiment and other calculations.

Slow growth is notoriously problematic, because it only gives the true
free energy in the limit that you do it infinitely slowly. Otherwise
you're really measuring nonequilibrium work values, which are
connected to free energies but only in an average way (see the
Jarzynski relationship for a more recent discussion of this).

This could be a classic example of "just because a method gives
perfect agreement with experiment, you can't be sure it's giving the
correct value for the force field." In other words, since force fields
have their own limitations, we can't necessarily expect that when we
do things right, we'll get optimal agreement with experiment. In some
cases one may get better agreement with experiment by doing things
*wrong* than by doing them right. i.e., suppose the correct value for
the force field is actually off by 2 kJ/mol from the experimental
value. If you make a protocol mistake, there's roughly a 50% chance
(assuming the errors are randomly distributed!) that it will give you
a value that's closer to the experimental value than your original
value was.

> Now, when splitting this simulation into 3 steps (3x 3.2ns), where I
> switch the charges to zero in the first step (hardcore), morph the LJ
> and bonded in the second (softcore or hardcore) and switch the charges
> back on from zero in the third step (hardcore), all in solvent, the sum
> of the single contributions does NOT yield the same number as the
> "single-step switching".
> In vacuum, the work values I get from the single step process and from
> adding up the values from the 3-step process perfectly match.
>
> The topologies for all systems are the same (except +/- water) for the
> 1-step and the 3-step simulations.
>
> Now I'm a bit puzzled and can't get an idea, where this difference in
> the solvated system may come from. I exclude a problem due to softcore,
> cause I also simulated the 3-step process all hardcore...
>
> Any ideas?

I'm betting your problems are largely due to the fact you're doing
slow growth. Again, see the Jarzynski relationship; I especially
recommend his Phys. Rev. E. paper on convergence (2001?). It's also
worth noting that slow growth transformations in different directions
have different convergence properties, and with slow growth
(interestingly enough) particle insertion actually converges more
quickly than particle deletion. So you could try reversing the
direction of the transformations and see what happens. But again, slow
growth isn't recommended these days -- you should probably make sure
you have a very good reason for doing it and are aware of the
limitations.

Best,
David

> Regards
>
> --
> Maik Goette, Dipl. Biol.
> Max Planck Institute for Biophysical Chemistry
> Theoretical & computational biophysics department
> Am Fassberg 11
> 37077 Goettingen
> Germany
> Tel.  : ++49 551 201 2310
> Fax   : ++49 551 201 2302
> Email : mgoette[at]mpi-bpc.mpg.de
>          mgoette2[at]gwdg.de
> WWW   : http://www.mpibpc.gwdg.de/groups/grubmueller/
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